connection on a 3-bundle


\infty-Chern-Weil theory

Differential cohomology



For GG a Lie 3-group, a connection on a GG-principal 3-bundle coming from a cocycle g:XBGg : X \to \mathbf{B}G is a lift of the cocycle to the 3-groupoid of Lie 3-algebra valued forms BG conn\mathbf{B}G_{conn}

BG conn X g BG \array{ && \mathbf{B}G_{conn} \\ & {}^{\mathllap{\nabla}}\nearrow & \downarrow \\ X &\stackrel{g}{\to}& \mathbf{B}G }



The higher parallel transport of local 3-connections is considered in

Discussion in terms of Gray-categories is in

  • Wei Wang, On 3-gauge transformations, 3-curvature and Gray-categories (arXiv:1311.3796)

Examples of 3-connections obtained from fibrations of Courant algebroids are discussed in

  • Olivier Brahic, On the infinitesimal Gauge Symmetries of closed forms (arXiv)

A discussion of fully general local 3-connections is in

and the globalization is in

For a discussion of all this in a more comprehensive context see section xy of

See also connection on an infinity-bundle for the general theory.

Revised on January 6, 2017 02:32:28 by Urs Schreiber (